Type the six digits
The machine shows six digits and a link to this page. Nothing is registered until you have seen which machine those digits belong to and said yes to it: they prove a machine is in front of you, and never that it is yours.
Sign in with GitHub, and this service is told which account you are - by number, never by name - and which address GitHub has confirmed. It asks for nothing else.
Google is the other way in the design names, and its OAuth app does not exist yet, so Google answers that it is not configured. There is no third way in, and this page will not make one.